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GATE 2024 Communication Systems Rank Booster Quiz 35
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Question 1
The probability density function of a random variable x is shown in figure below
If another random variable Y = 2X, then PDF for Y will be,
Question 2
The PDF of a random variable is fx(x) = ke–bx for x > 0
= 0 for x < 0, and k, b > a
Then k = bP, what is value of P?
Question 3
Consider an LTI system with impulse response given as 
. A wide-sense stationary (WSS) random process 
with autocorrelation function 
, is applied to the input of the above-mentioned system. Find the autocorrelation of the output signal 
if its given that ‘A’ and ‘a’ are real positive constants.
. A wide-sense stationary (WSS) random process with autocorrelation function , is applied to the input of the above-mentioned system. Find the autocorrelation of the output signal if its given that ‘A’ and ‘a’ are real positive constants. Question 4
For a random process X(t), if the mean is given by 2 and the auto-correlation function is
Rxx(t1,t2)= 5 + 2e-0.1|t1-t2|
Then, the covariance between X(5) and X(2) is _________.
Question 5
A binary baseband digital communication system employs the signal
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be
Question 6
A random binary wave y(t) is given by
Where p(t) = u(t) – u(t –T), u(t) is the unit function and f is an independent random variable with uniform distribution in [0, T]. The sequence {Xn} consists of independent and identically distributed binary valued random variables with P{Xn = +1} = P{Xn = –1} = 0.5 for each n.
The value of autocorrelation
equals______.
Where p(t) = u(t) – u(t –T), u(t) is the unit function and f is an independent random variable with uniform distribution in [0, T]. The sequence {Xn} consists of independent and identically distributed binary valued random variables with P{Xn = +1} = P{Xn = –1} = 0.5 for each n.
The value of autocorrelation
equals______.Question 7
An LTI system has a wide-sense stationary (WSS) input signal with zero mean. Its output is
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Dec 22ESE & GATE EC
